| dbo:abstract |
The Knaster–Kuratowski–Mazurkiewicz lemma is a basic result in mathematical fixed-point theory published in 1929 by Knaster, Kuratowski and Mazurkiewicz. The KKM lemma can be proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem. (en) En mathématiques, et plus précisément en topologie algébrique, le lemme de Knaster-Kuratowski-Mazurkiewicz, ou lemme KKM, est un résultat de point fixe publié en 1929 par Bronisław Knaster, Kazimierz Kuratowski et Stefan Mazurkiewicz. (fr) 수학에서 크나스테르-쿠라토프스키-마주르키에비치 덮개(Knaster-Kuratowski-Mazurkiewicz덮개, 영어: Knaster–Kuratowski–Mazurkiewicz cover)는 특정한 조건을 만족시키는, 단체의 닫힌집합으로 구성된 덮개이다. 구체적으로, 단체의 (꼭짓점의 부분 집합의 볼록 폐포인) 부분 단체는 각 꼭짓점에 대응되는 닫힌집합들로 덮혀져야 한다. 크나스테르-쿠라토프스키-마주르키에비치 정리(Knaster-Kuratowski-Mazurkiewicz定理, 영어: Knaster–Kuratowski–Mazurkiewicz theorem)에 따르면, 모든 크나스테르-쿠라토프스키-마주르키에비치 덮개는 적어도 하나 이상의 점을 공유한다 (즉, 그 교집합은 공집합이 될 수 없다). (ko) |
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| rdfs:comment |
The Knaster–Kuratowski–Mazurkiewicz lemma is a basic result in mathematical fixed-point theory published in 1929 by Knaster, Kuratowski and Mazurkiewicz. The KKM lemma can be proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem. (en) En mathématiques, et plus précisément en topologie algébrique, le lemme de Knaster-Kuratowski-Mazurkiewicz, ou lemme KKM, est un résultat de point fixe publié en 1929 par Bronisław Knaster, Kazimierz Kuratowski et Stefan Mazurkiewicz. (fr) 수학에서 크나스테르-쿠라토프스키-마주르키에비치 덮개(Knaster-Kuratowski-Mazurkiewicz덮개, 영어: Knaster–Kuratowski–Mazurkiewicz cover)는 특정한 조건을 만족시키는, 단체의 닫힌집합으로 구성된 덮개이다. 구체적으로, 단체의 (꼭짓점의 부분 집합의 볼록 폐포인) 부분 단체는 각 꼭짓점에 대응되는 닫힌집합들로 덮혀져야 한다. 크나스테르-쿠라토프스키-마주르키에비치 정리(Knaster-Kuratowski-Mazurkiewicz定理, 영어: Knaster–Kuratowski–Mazurkiewicz theorem)에 따르면, 모든 크나스테르-쿠라토프스키-마주르키에비치 덮개는 적어도 하나 이상의 점을 공유한다 (즉, 그 교집합은 공집합이 될 수 없다). (ko) |
| rdfs:label |
Lemme de Knaster-Kuratowski-Mazurkiewicz (fr) Knaster–Kuratowski–Mazurkiewicz lemma (en) 크나스테르-쿠라토프스키-마주르키에비치 덮개 (ko) |
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